1. Field of the Invention
This invention relates to hysteresis current controllers for reluctance machines.
2. Description of Related Art
The switched reluctance machine is an example of an electrical load having a variable inductance. It comprises a stator, defining stator poles, and a rotor, defining rotor poles. Energizing windings are wound in relation to the stator poles. Typically, groups of the windings are energized simultaneously as a phase. Energization of the windings of the or each phase is controlled by switching a source of electrical power in a phase circuit including the phase windings. The reluctance machine can be operated as either a motor or a generator. A description of switched reluctance machines and their control can be found in the article `The Characteristics, Design and Applications of Switched Reluctance Motors and Drives` by Stephenson and Blake, incorporated herein by reference in its entirety and presented at the PCIM '93 Conference and Exhibition at Nurnberg, Germany, Jun. 21-24, 1993.
At low speed, the torque developed by the switched reluctance motor is usually controlled by adjusting the amount of current in the phase windings, i.e. the motor is said to be "current fed". Usually, a voltage source is the most practicable means of deriving electrical power and so a current controller is required. The current controller controls the states of power switches to apply a voltage across the phase winding so as to establish the required current in the phase winding. The performance of the current controller, in both transient and steady-state sense, will be affected by the nature of the electrical load which the phase circuit presents. Unlike d.c. and induction motors, the winding of the switched reluctance machine has neither a constant inductance nor exhibits a simple `motional EMF` effect. A mathematical expression for the electrical behavior of the switched reluctance phase circuit can be described as: EQU v=iR+1(i,.theta.)di/dt+i.omega..differential.L/.differential..theta.(i,.the ta.) (1)
where:
v is the phase voltage PA1 R is the phase resistance PA1 i is the phase current PA1 L is the phase inductance PA1 1 is the incremental phase inductance PA1 .omega. is the rotational speed PA1 .theta. is the rotor angle relative to the stator PA1 the first term (iR) is that due to the resistive voltage drop in the phase winding; PA1 the second term (1(i,.theta.) di/dt) is proportional to the rate of change of phase current and is due to the effective inductance of the phase, i.e. the incremental inductance. This term can be seen to be nonlinear in nature as the incremental inductance is a function of both current and angle. A plot showing the variation in the incremental inductance of a sample switched reluctance machine is shown in FIG. 1 of the drawings which is a graph of incremental inductance against rotor angle for various values of phase current. This shows that incremental inductance can vary by over 10 to 1 for a machine operated over a wide range of currents, for example a servo-drive; PA1 the last term of equation (1) (i.omega..differential.L (i,.theta.)/.differential..theta.) can be seen to be proportional to the rotational speed (.omega.) and is therefore sometimes called the "motional EMF". It arises because the phase inductance is a function of rotor angle and therefore varies with time as the machine rotates. It is also nonlinear in nature and depends on how the phase inductance varies with rotor angle at a particular phase current and rotor angle. By way of illustration, FIG. 2 shows the motional EMF for a switched reluctance machine for a given speed and various values of phase current. PA1 f is the switching frequency PA1 V is the DC link voltage PA1 i.sub.av is the average phase current PA1 R is the phase resistance PA1 .epsilon.is the `motional EMF` PA1 l is the incremental inductance PA1 i.sub.h is the width of the hysteresis band
The three different terms in equation (1) may be explained as follows:
One form of current control which is often used with switched reluctance machines is hysteresis current control. It is widely used due to the high bandwidth control attainable and the simplicity of its implementation. Forms of hysteresis current control are described in EP-A-0635931, for example, which is incorporated herein by reference.
Hysteresis current control works by changing the conductive state of power switches in the current controller whenever the current reaches a threshold level above or below the demanded current. The gap between the upper and lower thresholds is known as the hysteresis band. A simple hysteresis current control function is shown in the graph of FIG. 3 where the voltage applied is of a constant magnitude, but opposite polarity, for the on and off states of the power switches and the current is assumed to rise and fall in a linear manner. In practice, this is not the case but serves to illustrate generally the hysteresis chopping waveform in which the current is free to vary within the limits of the upper and lower thresholds and is controlled by switching if it exceeds either threshold.
Simplified expressions for the on and off times (shown in FIG. 3 as t.sub.on and t.sub.off) may be used to derive the following equation: EQU f=(V.sup.2 -i.sup.2.sub.av -R.sup.2 -2i.sub.av R.epsilon.-.epsilon..sup.2)/2li.sub.h V (2)
where:
Equation (2) assumes that the instantaneous phase current will rise and fall in a linear manner as stated above. While this is not completely accurate, provided the switching period is short compared with the time constant of the inductive load (which is usually the case for a switched reluctance machine) the error due to this approximation to linearity is acceptably small.
It can be seen from equation (2) that the switching frequency will vary according to the particular phase circuit parameters unless the width of the hysteresis band is adjusted accordingly. In practice, this is not done as it would require the storage of significant amounts of data based on the electromagnetic characteristics of the machine. It would also require the sensing of rotor position and speed, in addition to current, and very rapid data processing to determine the correct width of the hysteresis band. Thus, when conventional hysteresis current control is used, the power switching frequency varies and undesirable acoustic noise often results.
In the simplest form of hysteresis current control, a fixed hysteresis band is used, centered around the demanded current. It is set to ensure that the power switching frequency is such that the maximum acceptable switching losses are not exceeded under any operating conditions of the drive. For example, in a positioning servo-drive based on a switched reluctance machine which is required to operate into overload, this will necessitate having a comparatively wide hysteresis band to cope with the very low incremental inductance encountered at high currents. This in turn can cause significant steady-state error at low average currents, because the positive and negative excursions about the demand current become unequal as soon as the lower bound of the hysteresis band reaches zero current.